I'm not sure that I can help you very much, but I will tell you what I do know.
I know that Rensellaer Adsit was born on November 4, 1808 in Albany County, New York.There is a Rensselaerville in Albany County, and it is 35 miles from Canajohrie (where Samuel was born on 9-11-1790) in Montgomery County, New York.Also, the county to the East of Albany is Rensselaer County.
I also know that Rensellaer's parents (whoever they may be) left New York in about 1812, and settled in Warren County, Ohio.In 1837 Rensellaer moved to Boone County, Indiana, and then in 1853 he moved to Iroquois County, Illinois.
Samuel Adsit did not leave New York until 1826, at which time he moved to Clinton County, Ohio.Clinton County is adjacent to Warren County.Then in about 1831, Samuel moved to Adams County, Indiana.Adams County & Boone County are not near to each other.Finally, around 1850, Samuel moved to Iroquois County, Illinois.
If we want to speculate, then perhaps Rensellaer is a son of Samuel's older brother James (born 12-22-1783) & his wife Phoebe Boyce?This would mean that when Samuel left New York, he was following in the footsteps of his brother who had left 14 years before, and it would be that Rensellaer is Samuel's nephew.
At any rate, it seems a safe assumption to say that Rensellaer is a Grandson or a Great-Grandson of Samuel Adsit and Abigail Kenyon who were the Adsits that left Connecticut and settled in Dutchess County, New York about 1760.
William Adsit was born around 1811, and was a "cousin" of Rensellaer Adsit.I don't know whether that was intended to mean literal first cousin, or simply to express that they were relatives.So, if Rensellaer is a son of James then maybe William is a son of James & Samuel's brother Silas (born 2-15-1793)& perhaps Silas and James had traveled together to Ohio, and Samuel wasn't quite ready to leave home at the time.
All of my speculations, are just that--speculations.If you have any other information that could help us sort this out, I would appreciate receiving it.